Lipschitz and bilipschitz maps on Carnot groups
نویسندگان
چکیده
منابع مشابه
lipschitz groups and lipschitz maps
this contribution mainly focuses on some aspects of lipschitz groups, i.e., metrizable groups with lipschitz multiplication and inversion map. in the main result it is proved that metric groups, with a translation-invariant metric, may be characterized as particular group objects in the category of metric spaces and lipschitz maps. moreover, up to an adjustment of the metric, a...
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The Hölder continuity of a harmonic function is characterized by the growth of its gradient. We generalize these results to solutions of certain subelliptic equations in domains in Carnot groups.
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A natural generalization of analytic functions to n-dimensional Euclidean space are quasiregular mappings.(See [2] and [3].) An analogue of Theorem 1.1 for quasiregular mappings in John domains in Euclidean space appeared in [4]. Recently the analytical tools used in the proof of this result have been generalized to Carnot groups. We give an account of some of these advances and obtain an analo...
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We consider the definition and regularity properties of convex functions in Carnot groups. We show that various notions of convexity in the subelliptic setting that have appeared in the literature are equivalent. Our point of view is based on thinking of convex functions as subsolutions of homogeneous elliptic equations.
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We show that for any K -quasiconformal map of the upper half plane to itself and any ε > 0 , there is a (K + ε) -quasiconformal map of the half plane with the same boundary values which is also biLipschitz with respect to the hyperbolic metric.
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2013
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.2013.263.143